When people explain the difference between the modem and router, the standard answer is modem is connection to internet and router is connection between computers to share the internet line. I see ATT 2Wire Gateway modem actually not only connects the phone line but also outputs the signal to multi computers at home. So, it is the modem or router?

I read the specs and apparently this is both a modem and a router. But you need to be an AT&T subscriber. Do you have a dedicated DSL line? If so, then you do not need the phone filters.

I may be wrong but here is my understanding of it:

The modem connects you to the internet.
The router connects other computers to your network.
Some modems are also a combination of modem and router. I think the term for these is "Gateway". I used to have a Linksys from Verizon that worked as a modem and a wireless router and they referred to it as a Gateway.

Your ATT modem/router connects you to the internet and puts out a signal for your network if you wanted to set one up.

The 2Wire Gateway devices are both a modem (in that it's the connection endpoint between your home and the provider) and a router (in that it can allow multiple computers to share the Internet connection at your home).

Other providers may use two separate devices to achieve the same thing - A DSL or cable modem that connects back to the provider, and a router that allows the customer to share that single line to their home with different computers or devices.

You can use a router that is not connected to the Internet - The computers connected to the router can connect to each other to share files or stream media content.

You typically can also connect a computer directly into your provider's modem for Internet access (although that is not usually recommended anymore in a home use situation).

Modems convert digital signals to auditory signals so that they could be sent over POTS(Plane Old telephone System) lines. DSL modems are not true modems but endpoint devices that enable your network traffic to interface with the DSL carrier, DSL is a digital signal that is carried on POTS lines along with the analogue voice signal.. Routers inspect header and other information and determine if the packet or data should be dent to an internal network address (a printer or another computer or device) or external network address (Internet). In a home unit you may have functions from three or more devices in one unit a modem or endpoint, a router, switch and firewall. Your two Wirer unit is one such device depending on the model, it can work as a wireless access point, switch router and endpoint.Having one unit makes installation easier and cheaper. These multi function units usually provide a good level of features and services and work well in the home, home office environment.